Question: Solve for $x$ and $y$ using elimination. ${-2x-6y = -44}$ ${2x+5y = 38}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $-y = -6$ $\dfrac{-y}{{-1}} = \dfrac{-6}{{-1}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {-2x-6y = -44}\thinspace$ to find $x$ ${-2x - 6}{(6)}{= -44}$ $-2x-36 = -44$ $-2x-36{+36} = -44{+36}$ $-2x = -8$ $\dfrac{-2x}{{-2}} = \dfrac{-8}{{-2}}$ ${x = 4}$ You can also plug ${y = 6}$ into $\thinspace {2x+5y = 38}\thinspace$ and get the same answer for $x$ : ${2x + 5}{(6)}{= 38}$ ${x = 4}$